Starting Values for Resolution of Trilinear Mixtures: Application in Spectroscopy

Donald S. Burdick, Xin M. Tu
Duke University, Harvard University

Oct 8 1991

Recent methodological development in three-way array analysis allows unique resolution of multicomponent linear mixtures in the absence of noise. When noise is present, an iterative linearization procedure based on least squares formulation was proposed by Appelof and Davidson, but it requires good initial guesses which may be difficult to find in practical situations. In this paper, we describe and alternative procedure based on eigenanalysis and discuss the relationship between the two procedures. Even though the alternative procedure does not aim to minimize the squared residuals, it is, however, non-iterative and may be used to find the initial values for the least squares procedure. An example using the phase resolved fluorescence spectroscopy data seems to indicate that only minor improvement may be expected from using the least squares procedure and for practical purposes the estimates from the eigenanalysis procedure may be close enought to dispense with the least squares procedure.


Nonlinear least squares, eigenanalysis, resolution of tilinear mixtures, phase-resolved, fluorescence spectrometry, alternating least squares


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